NEWTON — Moments after winning a Republican primary on Thursday, congressional candidate Sean Bielat made clear that his campaign intends to cast his general election opponent, Democrat Joseph P. Kennedy III, as an unqualified upstart aiming to coast to Congress on the value of his family name.

“What we do have is a deep belief that, in this country, being born isn’t enough to succeed,” Bielat, a 37-year-old officer in the Marine Corps Reserve, told about 100 supporters at the Crowne Plaza hotel. “It should take hard work. It should take effort. It should take merit.”

Bielat’s wife, Hope, said she, too, relished a fight against Kennedy, a 31-year-old former prosecutor and son of a former congressman.

“Sean may be an underdog in this race because he lacks the deep pockets, the celebrity, the political connections that go along with being a Kennedy,” she said. “But Sean is qualified for the job. He knows how to earn the American dream.”

Kennedy, who addressed supporters at the Elks Club in Taunton, rejected the notion that he is running on his famous name. He pointed to his work as a prosecutor, Peace Corps volunteer, and onetime worker in the legal aid bureau at Harvard Law School. Those jobs, he said, helped him serve people who felt the deck had been stacked against them.

“I’m proud of my record and I’m happy to stand on it,” he said in an interview. But, he said, “this campaign has been and is going to be about the issues,” including the economy, retirement security, and health care.

Bielat and Kennedy, who are vying to fill the House seat Barney Frank is leaving, emerged victorious from a series of congressional primaries Thursday.

Secretary of State William F. Galvin said turnout statewide was not expected to have topped 15 percent because only a few races were hotly contested. In addition, the election was not held on the traditional Tuesday, to avoid a conflict with Rosh Hashana, the Jewish New Year.

Many of the primaries were overshadowed by the far more prominent battle between Senator Scott Brown, a Republican, and Elizabeth Warren, a Democrat, which will be decided in November.

In a contested Democratic primary, Representative William R. Keating, who was elected to Congress two years ago, defeated C. Samuel Sutter, the Bristol district attorney, who struggled to differentiate himself from the incumbent because the two share many of the same views. Keating won with about 60 percent of the vote.

In November, Keating will face the winner of the GOP primary between Christopher Sheldon, 34, of Plymouth, and Adam Chaprales, 28, of Barnstable. That race was too close to call late Thursday night.

In another Democratic primary, Representative Richard E. Neal, a 12-term congressman from Springfield, parlayed his years of experience into a decisive victory against Andrea F. Nuciforo Jr., the register of deeds for the Berkshire Middle District, and Bill Shein, a writer from Alford.

Representative Niki Tsongas, a Lowell Democrat, was unopposed in her party’s primary. In November, she will face Jonathan A. Golnik, a Carlisle Republican, who challenged Tsongas two years ago. Golnik won his Republican primary against Thomas J.M. Weaver, a nuclear engineer from Westford.

Representative James P. McGovern, a Worcester Democrat, won his Democratic primary by defeating William Feegbeh. He will be unopposed in November.

Representative Edward J. Markey, a Malden Democrat, was unopposed in the Democratic primary and, in November, will face the winner of a Republican primary between three little-known candidates.

Representative Stephen F. Lynch, a South Boston Democrat, was also unopposed on Thursday. In November, he will face Joe Selvaggi, who won a Republican primary against Matias Temperley, an Iraq War veteran.

The national parties all but ignored the primaries that were decided on Thursday, instead focusing their resources on the general election fight between Richard R. Tisei, a Republican, and Representative John F. Tierney, a Salem Democrat.

Bielat, for one, will begin the general election at a steep financial disadvantage. The most recent fund-raising reports show he had just $63,000 cash on hand, compared with Kennedy’s $1.96 million.

But Bielat will undoubtedly try to use Kennedy’s name to raise money from Republican donors nationwide, as he did when he ran against Frank. Whether he can count on support from the GOP establishment is another question.

Several prominent Republicans, including former governor William F. Weld, endorsed one of Bielat’s primary opponents, Elizabeth Childs, a Brookline psychiatrist who served as mental health commissioner in the Romney administration.

Weld recorded an automated phone call for Childs in which he praised her as a social moderate and fiscal conservative not unlike himself. But in a Republican primary that draws partisan voters, Childs faced doubts about her allegiance to the party.

A former Democrat, she first registered as a Republican in July 2011. Bielat, by contrast, had more name recognition and good will among Republicans after mounting an aggressive but ultimately unsuccessful race against Frank.

The third candidate in the Republican primary, David L. Steinhof, a Fall River dentist, emphasized his conservative values, but never gained traction. Bielat captured more than 70 percent of the vote.

Kennedy captured about 90 percent of the vote in the Democratic primary for Frank’s seat. He crushed Rachel Brown, a follower of Lyndon Larouche who warned that President Obama was leading the world to thermonuclear war, and Herb Robinson, a musician and engineer from Newton.

Stephanie Ebbert of the Globe staff contributed to this report Michael Levenson can be reached at mlevenson@globe.com. Follow him on Twitter @mlevenson.

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